Detail from Portrait of a Woman inspired by Lucretia, by Lorenzo Lotto
Photograph: Alamy

Lorenzo Lotto lived in an age when artists and doctors were digging under the surface of human life. Leonardo da Vinci spent his nights dissecting and drawing the dead. The Padua-based surgeon Vesalius would publish a revolutionary – and gorily illustrated – book of human anatomy in 1543. That new knowledge glistens in the shaven scalp of a friar portrayed by Lotto in about 1526. You can see blue veins under the translucent skin of his forehead.

Spiritual fire … Portrait of a Dominican Friar from the Convent at San Zanipolo, 1526. Photograph: Musei Civici di Treviso

The friar’s name was probably Marcantonio Luciani, treasurer of the Venetian convent of Santi Giovanni e Paolo. His head is an oval of glistening intensity, the skin stretched taut over a cranium the artist seems not just to have looked at but run his hands over. Yet it isn’t just the precise observation of skin and bone that makes this portrait so magnetic. Luciani gazes at us full of spiritual fire. His head is a cannonball of idealism.

Intensity blazes in the eyes of all of Lotto’s dreamers, lovers and zealots. A young woman with her brown hair flattened under a fluffy white headdress, wearing a puffy tan and green dress that spreads out to fill the canvas, is holding up a print of the Roman heroine Lucretia, who stands, almost naked, preparing to stab herself. The Roman historian Livy told how Lucretia killed herself after being raped by the tyrant Tarquin. This painting is a study in the very possibility of action by women in a world that saw them as powerless. The role of Lucretia is ambiguous: at once an example of autonomy, and of loyalty to the patriarchal value of female chastity. What makes Lotto’s great portrait so subtle is that this woman is acting the part, trying it on for size. She has been reading – or writing out – Livy’s history in Latin, for it is quoted on a sheet of paper on her table, next to a sprig of flowers that could be a lover’s gift. So it looks as if she is asserting her purity in the context of a love affair. Cocking her head and engaging us with a direct and challenging look, she uses history to invent herself.

What is a self, anyway? The art of this Renaissance portraitist goes beyond copying what people looked like. Famous faces are few in this exhibition – many of the names are lost to time. It’s not like looking at Holbein’s portraits and marvelling at Henry VIII’s codpiece. The thrill of this exhibition is philosophical. Lotto is our contemporary. He is fascinated by identity – by what makes us who we are. Do we make ourselves or are we born this way?

Lotto was born in Venice in about 1480 and grew up as the portrait itself did. In 1501-02 his Venetian elder Giovanni Bellini painted a revolutionary portrait of Leonardo Loredan. In 1503, Leonardo da Vinci started the Mona Lisa. Lotto built on their examples to paint people with acute psychological drama and sophisticated realism. His earliest surviving portrait dates from the end of the 15th century. This sensual face of a dreamy-eyed young man imitates Bellini so closely it even captures his ethereal homoeroticism. Or is it Lotto’s own sensibility we’re seeing?

That’s hard to tell. While gossips wrote down salacious details about the sex lives of Leonardo, Bellini, and other stars of the Renaissance, no biographer was following Lotto on his patchy career in small north Italian cities. He never really made it in Venice and spent much of his career painting prominent locals in its subject city Bergamo. Sporadic successes never bought him security. There’s even a painting here that he gave his landlord in lieu of rent. He lived until 1556-57, dying in a religious community where he sought refuge from poverty.

No wonder sadness haunts his pictures. A young man in black who posed for Lotto in about 1530-32 displays all the symptoms of brooding melancholia. With his thin pale face over his dark jerkin, he studies a book while rose petals, which apothecaries prescribed for this affliction, are scattered on the table by him. Stranger still, a lizard scurries about – an eccentric pet? A symbol of sex or death? This youth could be Shakespeare’s Hamlet, portrayed 70 years before Shakespeare wrote his tragedy. Lotto does not laugh at his self-conscious melancholy. He feels for the lad.

There is so much feeling in this intimate encounter with Lotto’s world. One portrait comes with its “cover”, a rare survival of a 16th-century curiosity. Portraits half a millennium ago often had a second painting – in this case a landscape with a satyr – to hide them. You’d only remove the cover when you wanted to look at your lover or ancestor. It made a portrait a more private, sacred thing. An accurate image of a person still had a magical quality.

His masterpiece is one of the greatest portraits ever painted. Andrea Odoni, a Venetian art collector, stands with his hand on his heart among an array of ancient Roman sculptures. Odoni is painted with sensual warmth, his beard and long hair softly swaddling his face. He looks out of the painting with rapt passion as if willing us to share his love of antiquity. Like the woman posing as Lucretia, this is a proclamation of the classical ideal that inspired the Renaissance. Yet Lotto makes the stones and casts that surround Odoni as individual as he is. A head of the Emperor Hadrian rests by a headless, armless Venus. The muscular back of Hercules can be seen just behind Odoni. The nudes and fragments all seem components of Odini’s personality: the stuff out of which he sculpts himself. Is the head of a famously gay Roman ruler also a clue? Or are these just Lotto’s whimsies? This an exhibition of an artist with both intelligence and heart. Odoni has shored these fragments against his ruin. Lotto preserves him forever as a character in a play that is both comic and tragic in the theatre at which we’re all players.